How to multiply out a statement form? I got this form:

(not M or V) and (A or not M) and (not B or M) and (B or V) and (A or not V) and (not A or B)
Or: $$(\neg M\vee V) \wedge (A\vee\neg M) \wedge (\neg B \vee M) \wedge (B\vee V) \wedge (A\vee\neg V)\wedge(\neg A \vee B)$$

Can anyone explain me how to solve it step by step?
The result should be this:
A and B and M and V: $$A\wedge B \wedge M \wedge V$$
Wolfram Alpha link.
I dont know how to  simplify the statement
 A: $$(\neg M\vee V) \wedge \color{blue}{(A\vee\neg M)} \wedge (\neg B \vee M) \wedge \color{red}{(B\vee V) \wedge} \color{blue}{(A\vee\neg V)}\wedge \color{red}{(\neg A \vee B)}\tag{1}$$
$$\color{blue}{[A \lor (\lnot V \land \lnot M)]} \land \color{red}{[B \lor (\lnot A \land V)]} \land \color{green}{(\lnot B \lor M) \land (\lnot M \lor V)}\tag{2}$$
$${[A \lor (\lnot V \land \lnot M)]} \land {[B \lor (\lnot A \land V)]} \land \color{green}{(B \rightarrow M) \land ( M \rightarrow V)}\tag{3}$$
$$\vdots$$
$$A \land B\land M\land V\tag{result}$$
Note: 
To "deduce" this, I've highlighted some initial steps:


*

*$(1) \to (2)$ using 


*

*commutativity: $(P \lor Q) \equiv (Q \lor P)$ and $P \land Q \equiv Q \land P$,  

*associativity: $P\land (Q \land R) \equiv (P\land Q)\land R$,  

*distributive law (applied twice): $(P\lor Q) \land (P\lor R) \equiv P\lor (Q \land R)$, and 


*$(2)\to (3)$ using the identity ($\lnot P \lor Q) \equiv (P\rightarrow Q$), 

*It follows from $(3)$ (with more work needed to establish) that we must have $A$ and $B$; and since $B$, then also $M$; and since $M$, then also $V$. Why?



It also helps to use a truth-table, from which we can derive the conjunctive-normal form $(\text{result})$ of your expression given in $(1)$:

Note from the truth-table that the given expression evaluates to $\;T=$ true$\;$ only in the first row, if and only if $\;A,\text{ AND}\; B, \text{ AND}\;M, \text{ AND}\; V\;$ are all $\;T=$ true$\;$. That is, we can conclude: $$(\neg M\vee V) \wedge {(A\vee\neg M)} \wedge (\neg B \vee M) \wedge {(B\vee V) \wedge} {(A\vee\neg V)}\wedge {(\neg A \vee B)}$$ $$\iff A \land B \land M \land V$$

